Fiat said the cuts would be made across Opel's Europe-wide operations, which currently employ about 50,000.
Rival bidder, car parts maker Magna, pledged to keep Opel's four German plants, but made no comments about the two Vauxhall factories in the UK.
The third bidder is RHJ International, a Brussels-based investment firm.
German government officials are currently discussing the rival bids, submitted before Wednesday's deadline.
Unconfirmed reports suggest a fourth bid may have subsequently been tabled by a Chinese car firm, Beijing Auto.
Fiat added in its statement that reports it planned to cut up to 18,000 jobs in Germany, where Opel employs 25,000 people, were "entirely unfounded".
While most analysts still consider Fiat to be the front runner to buy Opel, and therefore become the world's second largest carmaker, a number of German politicians have already thrown their weight behind the offer from Canada's Magna.
This is because while Fiat has already warned that it would be likely to close one Opel factory in Germany - the engine plant at Kaiserslautern - Magna has vowed to keep open all four German Opel plants.
"Under our concept the German sites are seen as assets and we want to keep as many jobs as possible," said Magna co-chief executive Siegfried Wolf.
Roland Koch, the premier of Opel's home state of Hesse, said the Magna offer was "closest to the hopes and wishes" of German politicians and the country's Opel workers.
And German Foreign Minister Frank-Walter Steinmeier described the Magna bid as the only "sustainable" plan among the three.
Negotiations are continuing with all three parties, however, and Germany's economy minister said a host of questions remained about the Magna bid. He suggested a decision on Opel's future would be taken next week.
US giant General Motors (GM) is aiming to sell Opel ahead of a 1 June US government deadline to restructure its finances and avoid the need to go into bankruptcy protection.
GM is also looking to sell Sweden-based Saab, its other European car business.